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Sun, 02 Oct 2011 10:37:35 +0100Sun, 02 Oct 2011 10:37:35 +0100Efficient Computation of Equilibria in Bottleneck Games via Game Transformationhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2283
Thomas L. Werth; Heike Sperber; Sven O. Krumkereporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2283Thu, 10 Feb 2011 10:37:35 +0100Selfish Bin Coloringhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2145
We introduce a new game, the so-called bin coloring game, in which selfish players control colored items and each player aims at packing its item into a bin with as few different colors as possible. We establish the existence of Nash and strong as well as weakly and strictly Pareto optimal equilibria in these games in the cases of capacitated and uncapacitated bins. For both kinds of games we determine the prices of anarchy and stability concerning those four equilibrium concepts. Furthermore, we show that extreme Nash equilibria, those with minimal or maximal number of colors in a bin, can be found in time polynomial in the number of items for the uncapcitated case.Leah Epstein; Sven O. Krumke; Asaf Levin; Heike Sperberreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2145Fri, 16 Oct 2009 08:55:08 +0200Earliest Arrival Flows in Series-Parallel Graphshttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2137
We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs. In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.Stefan Ruzika; Heike Sperber; Mechthild Steinerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2137Tue, 06 Oct 2009 15:31:20 +0200How to find Nash equilibria with extreme total latency in network congestion games?https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2034
We study the complexity of finding extreme pure Nash equilibria in symmetric network congestion games and analyse how it depends on the graph topology and the number of users. In our context best and worst equilibria are those with minimum respectively maximum total latency. We establish that both problems can be solved by a Greedy algorithm with a suitable tie breaking rule on parallel links. On series-parallel graphs finding a worst Nash equilibrium is NP-hard for two or more users while finding a best one is solvable in polynomial time for two users and NP-hard for three or more. Additionally we establish NP-hardness in the strong sense for the problem of finding a worst Nash equilibrium on a general acyclic graph.Heike Sperberreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2034Wed, 29 Oct 2008 15:50:44 +0100